Trigonometric Ratios in Mathematics
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Questions and Answers

What is the value of tan Z?

  • 1.5
  • 0.8
  • 1.2 (correct)
  • 0.6

    • What is the value of cos C?

  • 0.4
  • 0.6
  • 0.7
  • 0.5 (correct)

    • What is the value of sin C?

  • 0.7
  • 0.5
  • 0.6 (correct)
  • 0.9

    • What is the value of tan X?

    <p>1.25</p> Signup and view all the answers

    What is the value of cos A?

    <p>0.6</p> Signup and view all the answers

    What is the value of sin A?

    <p>0.75</p> Signup and view all the answers

    What is the value of sin Z?

    <p>0.9</p> Signup and view all the answers

    What is the value of cos Z?

    <p>0.6</p> Signup and view all the answers

    What is the value of tan C?

    <p>1.0</p> Signup and view all the answers

    What is the value of sin B?

    <p>0.9</p> Signup and view all the answers

    What is the value of cos B?

    <p>0.6</p> Signup and view all the answers

    What is the value of tan A?

    <p>1.4</p> Signup and view all the answers

    What is the value of cos X?

    <p>0.8</p> Signup and view all the answers

    What is the value of sin X?

    <p>0.9</p> Signup and view all the answers

    What is the value of sin Z given the sides of the triangle?

    <p>0.8</p> Signup and view all the answers

    What is the value of cos A if side BC is 34 and AC is 40?

    <p>0.75</p> Signup and view all the answers

    What is the value of tan C for the given triangle?

    <p>0.4</p> Signup and view all the answers

    Determine the value of sin C if side AB is 17 and AC is 34.

    <p>0.4</p> Signup and view all the answers

    What is the value of cos Z if side YZ is 24 and YX is 30?

    <p>0.8</p> Signup and view all the answers

    Calculate the sine ratio for angle A from the triangle dimensions provided.

    <p>0.8</p> Signup and view all the answers

    What is the value of tan Z in the triangle described?

    <p>0.75</p> Signup and view all the answers

    Find the cosine value of angle C when sides measure AB = 16 and AC = 40.

    <p>0.4</p> Signup and view all the answers

    What is sin A given side lengths in the triangle?

    <p>0.75</p> Signup and view all the answers

    What is the correct value of tan X when considering the necessary sides?

    <p>0.4</p> Signup and view all the answers

    What is the value of cos C if AB is opposite and AC is the hypotenuse?

    <p>0.8</p> Signup and view all the answers

    Determine the sine value for angle B if side lengths are provided.

    <p>0.8</p> Signup and view all the answers

    Calculate the cosine for angle Z in the triangle measurements.

    <p>0.6</p> Signup and view all the answers

    Find the value of tan C given the lengths in the triangle.

    <p>0.8</p> Signup and view all the answers

    What is the sine of angle Z if sin Z=12/37?

    <p>0.32</p> Signup and view all the answers

    What is the cosine of angle C given that the adjacent side is 36 and hypotenuse is 45?

    <p>0.75</p> Signup and view all the answers

    What is the tangent of angle C if the opposite side is 50 and the adjacent side is 40?

    <p>1.25</p> Signup and view all the answers

    If angle A has a sine of 0.50, what could be its possible measure?

    <p>30 degrees</p> Signup and view all the answers

    If angle B has a cosine of 0.64, what is the approximate angle?

    <p>36 degrees</p> Signup and view all the answers

    Is it possible for the sine of an angle to equal 2 in a right triangle?

    <p>No, it must always be between -1 and 1.</p> Signup and view all the answers

    For an angle of 61 degrees, what is its cosine value?

    <p>0.48</p> Signup and view all the answers

    What is the sine of 38 degrees?

    <p>0.63</p> Signup and view all the answers

    What is the tangent of angle A if the opposite side is 21 and the adjacent side is 20?

    <p>1.05</p> Signup and view all the answers

    Given sin(48°) is to be calculated, which value is relevant?

    <p>0.74</p> Signup and view all the answers

    What is the value of $cos Z$ given the information?

    <p>0.8</p> Signup and view all the answers

    Calculate $tan C$ with the provided triangle sides.

    <p>1.3333</p> Signup and view all the answers

    What is the value of $sin 48°$?

    <p>0.7431</p> Signup and view all the answers

    Determine the value of $cos 61°$.

    <p>0.4848</p> Signup and view all the answers

    What is the value of $sin 38°$?

    <p>0.6157</p> Signup and view all the answers

    What is the calculated value of $tan A$?

    <p>1.05</p> Signup and view all the answers

    What is $sin Z$ if the triangle yields a value of 0.3243?

    <p>0.3243</p> Signup and view all the answers

    Calculate the value of $tan C$ based on the triangle dimensions.

    <p>0.3429</p> Signup and view all the answers

    What is the value of $cos 51°$?

    <p>0.6293</p> Signup and view all the answers

    What is the sine of angle Z with respect to $Z = 50$?

    <p>0.6</p> Signup and view all the answers

    Is it possible for the sine of an angle to equal 2?

    <p>No, the maximum value is 1.</p> Signup and view all the answers

    What is $tan X$ if $X = 40$ and $Z = 30$?

    <p>0.75</p> Signup and view all the answers

    Determine the value of $sin 50°$.

    <p>0.866</p> Signup and view all the answers

    What is the tangent of angle A calculated with the sides 40 and 30?

    <p>1.3333</p> Signup and view all the answers

    Study Notes

    Trigonometric Ratios

    • Trigonometric Ratios are used to find the relationships between the sides and angles of a right triangle.

    • SOH CAH TOA is a mnemonic device to remember the ratios:

      • SOH: Sine = Opposite / Hypotenuse
      • CAH: Cosine = Adjacent / Hypotenuse
      • TOA: Tangent = Opposite / Adjacent

    • Hypotenuse is the longest side of a right triangle and is always opposite to the right angle.

    • For each trigonometric ratio, the angle of reference needs to be specified.

    • Values of trigonometric ratios can be expressed as fractions or decimals (rounded off as needed).

    • Example: For a right triangle with angles A, B and C (where C is the right angle), and sides a, b and c (where c is the hypotenuse), the trigonometric ratio of sine of angle A is: sin A = a / c### Trigonometric Ratios

    • The tangent (tan) of an angle is equal to the opposite side divided by the adjacent side.

    • The sine (sin) of an angle is equal to the opposite side divided by the hypotenuse.

    • The cosine (cos) of an angle is equal to the adjacent side divided by the hypotenuse.

    Applications of Trigonometric Ratios

    • The tangent of an angle can be used to calculate the height of a building or tree when the distance from the building or tree is known.
    • The sine and cosine of an angle can be used to calculate the length of the sides of a right triangle when one side and one angle are known.

    Key Facts about Trigonometric Ratios

    • The sine of an angle can never be greater than 1 or less than -1.
    • The cosine of an angle can never be greater than 1 or less than -1.
    • The tangent of an angle can be any value between -infinity and infinity.

    Examples of Trigonometric Ratios

    • The tangent of angle C in triangle ABC is equal to 50/30, or 1.66.
    • The sine of angle Z in triangle XYZ is equal to 30/50, or 0.6.
    • The cosine of angle Z in triangle XYZ is equal to 40/50, or 0.8.

    Critical Thinking Question:

    • The sine of an angle can never be equal to 2 because it cannot be greater than 1.

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    Trigonometric Ratios PDF

    Description

    Explore the foundational concepts of trigonometric ratios used to determine the relationships within right triangles. This quiz covers important mnemonics like SOH CAH TOA, as well as detailed definitions and examples of sine, cosine, and tangent. Perfect for students looking to solidify their understanding of trigonometry.

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